TSTP Solution File: ROB010-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : ROB010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 20:54:44 EDT 2022
% Result : Unsatisfiable 0.61s 0.84s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ROB010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 15:19:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.61/0.84 % SZS status Unsatisfiable
% 0.61/0.84 % SZS output start Proof
% 0.61/0.84 The input problem is unsatisfiable because
% 0.61/0.84
% 0.61/0.84 [1] the following set of Horn clauses is unsatisfiable:
% 0.61/0.84
% 0.61/0.84 add(X, Y) = add(Y, X)
% 0.61/0.84 add(add(X, Y), Z) = add(X, add(Y, Z))
% 0.61/0.84 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X
% 0.61/0.84 negate(add(a, negate(b))) = c
% 0.61/0.84 negate(add(c, negate(add(b, a)))) = a ==> \bottom
% 0.61/0.84
% 0.61/0.84 This holds because
% 0.61/0.84
% 0.61/0.84 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.61/0.84
% 0.61/0.84 E:
% 0.61/0.84 add(X, Y) = add(Y, X)
% 0.61/0.84 add(add(X, Y), Z) = add(X, add(Y, Z))
% 0.61/0.84 f1(a) = false__
% 0.61/0.84 f1(negate(add(c, negate(add(b, a))))) = true__
% 0.61/0.84 negate(add(a, negate(b))) = c
% 0.61/0.84 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X
% 0.61/0.84 G:
% 0.61/0.84 true__ = false__
% 0.61/0.84
% 0.61/0.84 This holds because
% 0.61/0.84
% 0.61/0.84 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.61/0.84
% 0.61/0.84 add(X, Y) = add(Y, X)
% 0.61/0.84 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2))
% 0.61/0.84 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2))
% 0.61/0.84 add(add(X, Y), Z) -> add(X, add(Y, Z))
% 0.61/0.84 f1(a) -> false__
% 0.61/0.84 f1(negate(add(c, negate(add(a, b))))) -> true__
% 0.61/0.84 f1(negate(add(c, negate(add(b, a))))) -> true__
% 0.61/0.84 negate(add(a, negate(add(c, negate(negate(add(a, b))))))) -> c
% 0.61/0.84 negate(add(a, negate(b))) -> c
% 0.61/0.84 negate(add(c, negate(add(a, b)))) -> a
% 0.61/0.84 negate(add(c, negate(add(a, negate(negate(b)))))) -> a
% 0.61/0.84 negate(add(c, negate(add(negate(a), negate(b))))) -> negate(b)
% 0.61/0.84 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) -> X
% 0.61/0.84 negate(add(negate(add(Y0, Y1)), negate(add(negate(Y0), Y1)))) -> Y1
% 0.61/0.84 negate(add(negate(add(Y0, Y1)), negate(add(negate(Y1), Y0)))) -> Y0
% 0.61/0.84 negate(add(negate(add(Y0, c)), negate(add(Y0, add(a, negate(b)))))) -> Y0
% 0.61/0.84 negate(add(negate(add(Y1, Y0)), negate(add(Y0, negate(Y1))))) -> Y0
% 0.61/0.84 negate(add(negate(add(a, add(negate(b), Y1))), negate(add(Y1, c)))) -> Y1
% 0.61/0.84 negate(add(negate(add(negate(Y1), Y0)), negate(add(Y0, Y1)))) -> Y0
% 0.61/0.84 true__ -> false__
% 0.61/0.84 with the LPO induced by
% 0.61/0.84 f1 > b > c > a > negate > add > true__ > false__
% 0.61/0.84
% 0.61/0.84 % SZS output end Proof
% 0.61/0.84
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